The idea that the Iraq war is over is attractive but deeply misleading. Barack Obama, visiting the troops at Fort Bragg today, will scatter soil on the coffin of a conflict he never supported. The remaining US troops will be home for Christmas, thankful not to be carried back along with 4,500-plus American dead. British forces and other coalition allies have long since departed – or given up the ghost. For the record, the gravestone marking this calamitous misadventure will duly read: "Iraq, 2003-2011. RIP."

But as Americans breathe a sigh of relief, the Iraqi reality is radically different. In Baghdad and Basra, in Ramadi and Mosul, and in Tehran, Riyadh, Damascus and Tel Aviv, unfinished business, much of it explosively dangerous and dating back to the era of Saddam Hussein, will come more sharply into focus as the clump-clump of retreating American boots fades away.

The US withdrawal, while hugely welcome, is inherently destabilising. It is not an ending, any more than was imperial Britain's exit from its African colonies. Rather, it marks the beginning of, and a possible spark for, the next stage of struggle. Iran's rulers understand this historic truth very well. And their view matters since, as many regional analysts believe, it was Tehran, not Washington, that "won" the war in Iraq.

Looming post-occupation flashpoints include endemic political division and economic weakness in Baghdad, the questionable capabilities of Iraq's rebuilt army and police forces amid ongoing security threats, the new Shia ascendancy and rising tensions with the previously dominant Sunnis, Kurdistan's de facto unilateral declaration of independence, intractable disputes over territory and oil and gas revenues, and the possible resurrection of al-Qaida in Mesopotamia. All these issues were created, or exacerbated, by George W Bush's decision to invade. And all continue to be ruthlessly exploited by Shia Iran, Iraq's historic enemy and now its daunting, over-bearing neighbour.

Iran's tentacles extend into the heart of the Iraqi political establishment, starting with the prime minister, Nouri al-Maliki, once a sheltered exile on Iranian soil and an advocate of close fraternal ties. Iran's interests are faithfully represented in parliament by the Sadrist followers of the hardline Shia leader Moqtada al-Sadr, and on the streets by his Mahdi army militia.

Iran is thought to run hundreds if not thousands of operatives inside Iraq, ranging from bone fide diplomats to spies and agents provocateurs. Its interest, the opposite of Washington's, is to keep Iraq weak, dependent and submissive. Its achievement, with a massive assist from the US, is to have eliminated Iraq as an obstacle or potential rival to its drive for regional superpower status.

At a White House meeting with Obama this week, Maliki vowed to rebuild Iraq's sovereignty and signalled interest in continuing American arms sales and military-to-military collaboration. In comments apparently aimed at Iran, he said Iraq would pursue a foreign policy "which does not intervene in the affairs of others and does not allow the others to intervene in its own affairs".

But it was this same Maliki who, egged on by Tehran, torpedoed US plans to maintain military bases in Iraq after 2011. And it is Maliki who now leads a country whose 700,000-strong security forces are incapable, according to US assessments, of defending it against external foes, principally Iran but also Turkey and an increasingly unpredictable Syria.

The Iraq war's unfinished business stretches way beyond its national boundaries. Its many disastrous miscalculations and negative consequences continue to reverberate around the world. The Bush administration's ill-founded insistence that Saddam colluded with al-Qaida, and even with the 9/11 attacks, seriously undermined whatever legitimacy the "war on terror" might have had. By creating a lawless Iraq, Bush allowed al-Qaida a foothold that Saddam had always denied it.

Bogus US claims about Saddam's weapons of mass destruction have had a similarly chilling impact on counterproliferation efforts. When Washington denounces Iran's nuclear activities, its words are greeted with undeserved scepticism in many quarters. The Iraq war's undermining of the cause of human rights and universal justice has also had a lasting effect. The Abu Ghraib torture and prisoner abuse smashed American credibility on this subject, at least for a time. It set a terrible double standard that has heartened anti-democrats everywhere, from Russia's Vladimir Putin to Syria's Bashar al-Assad.

The Iraq war continues, by proxy, in other theatres – for example, in the way the Sunni-led monarchies of the Gulf are consolidating their ties with Washington in opposition to what they see as a nascent Shia-dominated alliance embracing Iraq, Iran and Syria. The war continues for Turkey, too. Ankara refused in 2003 to allow US invasion troops to cross its territory. Since that watershed moment, Turkey has increasingly distanced itself from western and Israeli policy, notably on Iran and Palestine. Turkish forces regularly invade northern Iraq in pursuit of Kurdish militants. With the Americans gone, such confrontations may escalate.

The $700bn Iraq war, coming in tandem with Afghanistan and the financial crisis, decisively tipped the balance of power and advantage from the US to China. It split the EU, creating divisions that have hardened into permanent positions, as seen in Germany's Iraq-style refusal to support Nato's Libya campaign. But most damagingly of all, perhaps, the war's acid legacy continues to corrode belief in western democracy.

When Bush and his loquacious frontman, Tony Blair, made the case for the war, they repeatedly strained the truth, and sometimes lied outright. In betraying the public trust, they did incalculable harm to the western democratic tradition that is held up as a model for the rest of the world. This damage has not been repaired. Fault has not been fully admitted. Apologies have not been tendered. It's another reason why the Iraq war is not over and why, for generations living now, it possibly never will be.